$\dfrac{ 7j + 7k }{ -6 } = \dfrac{ 4j - 9l }{ -9 }$ Solve for $j$.
Answer: Multiply both sides by the left denominator. $\dfrac{ 7j + 7k }{ -{6} } = \dfrac{ 4j - 9l }{ -9 }$ $-{6} \cdot \dfrac{ 7j + 7k }{ -{6} } = -{6} \cdot \dfrac{ 4j - 9l }{ -9 }$ $7j + 7k = -{6} \cdot \dfrac { 4j - 9l }{ -9 }$ Multiply both sides by the right denominator. $7j + 7k = -6 \cdot \dfrac{ 4j - 9l }{ -{9} }$ $-{9} \cdot \left( 7j + 7k \right) = -{9} \cdot -6 \cdot \dfrac{ 4j - 9l }{ -{9} }$ $-{9} \cdot \left( 7j + 7k \right) = -6 \cdot \left( 4j - 9l \right)$ Distribute both sides $-{9} \cdot \left( 7j + 7k \right) = -{6} \cdot \left( 4j - 9l \right)$ $-{63}j - {63}k = -{24}j + {54}l$ Combine $j$ terms on the left. $-{63j} - 63k = -{24j} + 54l$ $-{39j} - 63k = 54l$ Move the $k$ term to the right. $-39j - {63k} = 54l$ $-39j = 54l + {63k}$ Isolate $j$ by dividing both sides by its coefficient. $-{39}j = 54l + 63k$ $j = \dfrac{ 54l + 63k }{ -{39} }$ All of these terms are divisible by $3$ Divide by the common factor and swap signs so the denominator isn't negative. $j = \dfrac{ -{18}l - {21}k }{ {13} }$